Paperboard tubes are widely used in the paper, film and textile industries to wind material as it is manufactured. These tubes are manufactured continuously by spirally winding multiple paperboard strips or plies around a stationary mandrel. Paperboard tubes are also made in a convolute winding process by forming a multiple layer wrap of a wide paperboard sheet around a stationary mandrel. Although paperboard is relatively weak on a single layer basis, a tube constructed from multiple spirally wound or convolute wound paperboard layers can attain substantial strength.
As with other materials, paperboard tubes exhibit different strength values depending on which strength characteristics are measured. These different strength characteristics, such as compressive strength, tensile strength, beam strength, etc., can vary according to tube construction. The standard industry test to evaluate strength of paper tubes is the flat crush test. This test involves compressing a tube along its sides by placing the tube between two flat plates. One plate is stationary while the other moves at a constant displacement rate transversely to the axis of the tube. The flat crush strength is the maximum load obtained during the test.
Paperboard is an orthotopic material. Thus, paperboard properties are different in the machine direction (MD) and in the cross machine direction (CD), wherein machine direction refers to the paper manufacturing process. The property difference between the MD and CD can be attributed to the tendency for more paper fibers to be aligned along the MD as compared to CD. The orthotopic properties of paper influence tube strength and complicate any accurate prediction of tube strength.
In addition, the paperboard strips used to prepare spirally wound paperboard tubes are wound at varying angles, and tube properties depend, at least in part, on the general angle of the spirally wound strips. This in turn, increases the difficulty in accurately predicting paperboard tube properties from theoretical principals. Recently, a closed-form elasticity solution has been developed to predict stresses and strains in spiral paper tubes loaded axisymmetrically. In experiments to verify this theory, a load was applied via fluid to the exterior periphery of a spirally wound paperboard tube so that the radial load was uniform around the circumference of the tube; see T. D. Gerhardt, "External Pressure Loading of Spiral Paper Tubes: Theory and Experiment", Journal of Engineering Materials and Technology, Vol. 112, pp. 144-150, 1990. As opposed to the situation analyzed in the 1990 study, flat crush loading is not uniform around the tube circumference. Therefore, flat crush stress distributions are much more complex than those resulting from the radial crush loading of the 1990 article.
It is generally understood that flat crush strength can be increased by increasing tube wall thickness and/or employing stronger paper plies for the layers of the spirally wound tube. In regard to the latter, paper is available in a wide variety of grades. In general, paper strength can be improved by mechanical refining of paperboard pulps. Thus, a well-beaten pulp generally produces a stronger grade of paper compared to a lightly beaten pulp. In addition, paper strength can be improved by compressing the paperboard during manufacture by running the web through a set of high pressure nip rolls. Further, paperboard strength is influenced by fiber type and quality. As a general rule, stronger paperboard sheets have a higher density than low strength paperboard sheets. Stated differently, the above treatments generally result in an increase in paperboard density along with the increase in paperboard strength. The higher density, higher strength papers are also more costly.
It is common in the paper tube industry to use more than one type of paperboard when fabricating a tube. This can be done for many reasons. For example, in some cases, a special surface finish is needed on the tube inside diameter (ID) or on the tube outside diameter (OD) and a paper ply having such a finish is therefore used on the OD or ID. Different grades of paper are also used in order to satisfy other special property requirements for the tube ID or OD such as, for example, as might be required for interaction with a chuck or other structure. At times, different paper grades are used simply to satisfy a wall thickness requirement or to reduce cost by using cheaper, lower strength paperboard in the tube and/or to compensate for lack of inventory of a certain ply width of paper.
Although multiple grades of paper have previously been used to produce spirally wound paperboard tubes, the multiple grades of paperboard have not in the past, to the knowledge of the present inventors, been positioned with the intent and effect of providing maximum flat crush strength. Moreover, such positioning is a relatively complex problem for the reasons discussed above; namely, that a paper tube is a complex, anisotropic structure. Moreover, the number of different possible ply position combinations for a multiple grade (multi-grade) paperboard tube is staggering even when a relatively few number of plies are used. Various assumptions have been relied on in the past in positioning different plies in paperboard tubes, and it is the inventors' understanding that a widely held view has been that flat crush strength can be enhanced by positioning high density paperboard plies on the exterior of the paperboard tube. Although various approaches have been used in the art in an attempt to use higher strength plies to improve flat crush strength of paperboard tubes, there is no known criteria according to which paperboard ply placement in a paperboard tube can be carried out to maximize flat crush strength with reliability.